scholarly journals The effect of noise on strange nonchaotic attractors

2000 ◽  
Vol 268 (4-6) ◽  
pp. 315-322 ◽  
Author(s):  
I.A. Khovanov ◽  
N.A. Khovanova ◽  
P.V.E. McClintock ◽  
V.S. Anishchenko
Keyword(s):  
Strange Nonchaotic Attractors

Strange Nonchaotic Trajectories on Torus

1997 ◽  
Vol 07 (02) ◽  
pp. 423-429 ◽  
Author(s):  
T. Kapitaniak ◽  
L. O. Chua
Keyword(s):  
Lebesgue Measure ◽  
Parameter Space ◽  
Positive Lebesgue Measure ◽  
Strange Nonchaotic Attractors

In this letter we have shown that aperiodic nonchaotic trajectories characteristic of strange nonchaotic attractors can occur on a two-frequency torus. We found that these trajectories are robust as they exist on a positive Lebesgue measure set in the parameter space.

Boundedness of a Class of Complex Lorenz Systems

2021 ◽  
Vol 31 (07) ◽  
pp. 2150101
Author(s):  
Xu Zhang
Keyword(s):  
Dynamical System ◽  
Current Literature ◽  
Chaos Control ◽  
Type Systems ◽  
Chaotic Attractors ◽  
Strange Nonchaotic Attractors ◽  
Control And Synchronization ◽  
Ultimate Bound

The estimate of the ultimate bound for a dynamical system is an important problem, which is useful for chaos control and synchronization. In this paper, the estimated ultimate bound of a class of complex Lorenz systems is provided, which extends the parameter regions identified in the current literature on this problem. Based on these results, a kind of complex Lorenz-type systems is constructed, which might have many or infinitely many strange nonchaotic attractors, chaotic attractors, or an infinitely-many-scroll attractor.

OLD AND NEW RESULTS ON STRANGE NONCHAOTIC ATTRACTORS

2007 ◽  
Vol 17 (11) ◽  
pp. 3895-3928 ◽  
Author(s):  
ÀNGEL JORBA ◽  
JOAN CARLES TATJER ◽  
CARMEN NÚÑEZ ◽  
RAFAEL OBAYA
Keyword(s):  
Differential Equations ◽  
Topological Structure ◽  
Base Flow ◽  
Skew Products ◽  
Almost Automorphic ◽  
Strange Nonchaotic Attractors

Classical and new results concerning the topological structure of skew-products semiflows, coming from nonautonomous maps and differential equations, are combined in order to establish rigorous conditions giving rise to the occurrence of strange nonchaotic attractors on 𝕋d × ℝ. A special attention is paid to the relation of these sets with the almost automorphic extensions of the base flow. The scope of the results is clarified by applying them to the Harper map, although they are valid in a much wider context.

APERIODIC NONCHAOTIC ATTRACTORS, STRANGE AND OTHERWISE

2007 ◽  
Vol 17 (10) ◽  
pp. 3397-3407 ◽  
Author(s):  
AWADHESH PRASAD ◽  
AMITABHA NANDI ◽  
RAMAKRISHNA RAMASWAMY
Keyword(s):  
New Developments ◽  
The Past ◽  
Excitable Systems ◽  
Potential Applications ◽  
The Creation ◽  
Strange Nonchaotic Attractors ◽  
Important Objective

The main conceptual issues in the study of strange nonchaotic dynamics have been summarized and reviewed earlier [Prasad et al., 2001]. In the past five years, there has been further progress in the analysis of such attractors, and in understanding the nature of dynamical transitions in quasiperiodically forced systems. Here we discuss new developments which include the creation of strange nonchaotic attractors in excitable systems, the elucidation of the mechanisms for the intermittent and fractalization routes to SNA as well as their potential applications. The possibility of creating such attractors without recourse to quasiperiodic forcing is an important objective, and this has been realized in specific circumstances.

Experimental distinction between chaotic and strange nonchaotic attractors on the basis of consistency

2013 ◽  
Vol 23 (2) ◽  
pp. 023110 ◽  
Author(s):  
Seiji Uenohara ◽  
Takahito Mitsui ◽  
Yoshito Hirata ◽  
Takashi Morie ◽  
Yoshihiko Horio ◽  
...  
Keyword(s):  
Strange Nonchaotic Attractors

RENORMALIZATION IN QUASIPERIODICALLY FORCED SYSTEMS

2003 ◽  
Vol 03 (02) ◽  
pp. L251-L258 ◽  
Author(s):  
A. H. OSBALDESTIN ◽  
B. D. MESTEL
Keyword(s):  
Localized States ◽  
Rigorous Results ◽  
Two Level Systems ◽  
Self Similar ◽  
Strange Nonchaotic Attractors ◽  
Harper Equation

We review our recent rigorous results on renormalization in a variety of quasiperiodically forced systems. Our results include a description of (i) self-similar fluctuations of localized states in the Harper equation, including the renormalization strange set (known as the orchid) in the generalized Harper equation; and (ii) self-similarities in the correlations of strange nonchaotic attractors, barrier billiards, and quantum two-level systems.

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